The geometric sequence $(a_i)$ is defined by the formula: $a_i = 1 \left(-\dfrac{1}{4}\right)^{i - 1}$ What is $a_{5}$, the fifth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $1$ and the common ratio is $-\dfrac{1}{4}$ To find $a_{5}$ , we can simply substitute $i = 5$ into the given formula. Therefore, the fifth term is equal to $a_{5} = 1 \left(-\dfrac{1}{4}\right)^{5 - 1} = \dfrac{1}{256}$.